Electrostatics – Class 12 Physics Notes (ISC)

1. Basic Concepts

Electric Charge (q): Fundamental property that causes electric interactions.
Unit: Coulomb (C), Quantized as q = n·e (e = 1.6×10⁻¹⁹ C).
Types: Positive and Negative. Like charges repel, unlike attract.

2. Coulomb’s Law

F = (1 / 4πε₀) × (q₁q₂ / r²)
ε₀ = 8.85 × 10⁻¹² C²/N·m²

3. Electric Field (E)

E = F / q₀
E = (1 / 4πε₀) × (q / r²)

Direction is outward for +q and inward for –q.

4. Electric Field Lines

• Begin on +ve, end on –ve charges.
• Never intersect.
• Density indicates field strength.

5. Electric Dipole

Dipole Moment (p) = q × 2a

Axial field: E = (1 / 4πε₀) × (2p / r³)
Equatorial field: E = (1 / 4πε₀) × (p / r³)

6. Electric Potential (V)

V = (1 / 4πε₀) × (q / r)
E = -dV/dr

7. Equipotential Surfaces

• Surfaces of equal potential.
• Perpendicular to electric field lines.
• No work done along them.

8. Capacitance (C)

C = q / V
For parallel plates: C = ε₀A/d
With dielectric: C = Kε₀A/d

9. Capacitor Combinations

Series: 1/Ceq = 1/C1 + 1/C2 + ...
Parallel: Ceq = C1 + C2 + ...

10. Energy in Capacitor

U = ½ CV² = q² / 2C = ½ qV

11. Gauss’s Law

Φ = ∮ E · dA = q_inside / ε₀

Used for point charges, line charges, and plane sheets.

12. Example

Two charges +3μC and –2μC are 0.5 m apart. Force between them:

F = 9 × 10⁹ × (3×10⁻⁶)(2×10⁻⁶) / (0.5)² = 0.216 N (Attractive)

🔌 Current Electricity – Class 12 Physics (ISC)

Magnetic Effects of Current and Magnetism
Class 12 Physics (ISC)

1. Introduction

Electric current produces a magnetic field around it. This phenomenon is called the magnetic effect of current. Magnetism deals with the forces and fields associated with magnets and magnetic materials.

2. Magnetic Field due to a Current-Carrying Conductor

The magnetic field lines around a straight current-carrying conductor are concentric circles with the conductor at the center.

Right-Hand Thumb Rule

To find the direction of the magnetic field, hold the conductor with your right hand such that the thumb points in the direction of current. The curled fingers show the direction of the magnetic field lines.

3. Magnetic Field due to a Circular Loop

The magnetic field at the center of a circular current-carrying loop of radius r carrying current I is given by:

B = (μ₀ I) / (2r)

where μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space.

4. Magnetic Field due to a Solenoid

A solenoid is a coil of many turns of wire. The magnetic field inside a long solenoid is uniform and is given by:

B = μ₀ n I

where n is the number of turns per unit length and I is the current.

5. Force on a Current-Carrying Conductor in a Magnetic Field

A conductor carrying current placed in a magnetic field experiences a force given by:

F = BIL sin θ

• B = Magnetic field strength (Tesla)
• I = Current (Ampere)
• L = Length of conductor in the field (m)
• θ = Angle between conductor and magnetic field

Direction of Force: Fleming’s Left-Hand Rule

Thumb: Force (motion)
Forefinger: Magnetic Field (North to South)
Middle Finger: Current (Positive to Negative)

6. Magnetic Force between Two Parallel Conductors

Two parallel current-carrying conductors exert a force on each other:

• If currents are in the same direction, force is attractive.
• If currents are opposite, force is repulsive.

Magnitude of force per unit length is:

F/L = (μ₀ / 2π) (I₁ I₂ / d)

where d is distance between conductors.

7. Magnetic Properties of Materials

Materials respond to magnetic fields differently:

• Diamagnetic: Weakly repelled by magnetic fields (e.g., copper, bismuth)
• Paramagnetic: Weakly attracted by magnetic fields (e.g., aluminum, platinum)
• Ferromagnetic: Strongly attracted, can be permanently magnetized (e.g., iron, cobalt, nickel)

8. Earth’s Magnetism

The Earth behaves like a huge magnet with magnetic poles near the geographic poles.

• Magnetic Declination: Angle between geographic north and magnetic north.
• Magnetic Inclination: Angle made by Earth’s magnetic field with horizontal.

9. Electromagnet

An electromagnet is a soft iron core wrapped with a coil carrying current. It acts as a temporary magnet whose strength can be controlled by changing current or number of turns.

10. Applications of Magnetic Effects of Current

• Electric motors
• Generators
• Relays and contactors
• Galvanometers and ammeters
• Magnetic storage devices

Electromagnetic Induction
Class 12 Physics (ISC)

1. Introduction

Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (emf) in a conductor.

2. Faraday’s Laws of Electromagnetic Induction

1. First Law: Whenever the magnetic flux linked with a coil changes, an emf is induced in the coil.
2. Second Law: The magnitude of induced emf is equal to the rate of change of magnetic flux through the coil.
   ε = - dΦ/dt

3. Magnetic Flux (Φ)

Magnetic flux through an area A in a magnetic field B at an angle θ is:

Φ = B A cos θ

4. Lenz’s Law

The direction of the induced emf (and hence induced current) is such that it opposes the change in magnetic flux that produced it.

5. Eddy Currents

Circular currents induced in bulk conductors when exposed to a changing magnetic field are called eddy currents. They cause energy loss in transformers and brakes in trains.

6. Self-Induction

A changing current in a coil induces an emf in the same coil opposing the change. This is called self-induction.

Self-induced emf, ε = -L (dI/dt), where L is the self-inductance.

7. Mutual Induction

A changing current in one coil induces emf in a nearby second coil. This is mutual induction.

Mutual induced emf, ε = -M (dI/dt), where M is the mutual inductance.

8. Applications

• Electric generators
• Transformers
• Induction cooktops
• Electric brakes
• Wireless charging

9. Important Formulas

Alternating Current (AC)
Class 12 Physics (ISC)

1. Introduction

Alternating current (AC) is an electric current which periodically reverses its direction, unlike direct current (DC) which flows only in one direction.

2. AC Voltage and Current

The instantaneous value of AC current or voltage varies sinusoidally with time and can be expressed as:

i = Im sin(ωt)    or    v = Vm sin(ωt)

• Im = Maximum (peak) current
• Vm = Maximum (peak) voltage
• ω = 2πf is angular frequency (rad/s)
• f = Frequency (Hz)
• t = Time (seconds)

3. RMS (Root Mean Square) Values

RMS value of AC current or voltage gives the equivalent DC value producing the same heating effect.

Irms = Im / √2    and    Vrms = Vm / √2

4. Frequency and Time Period

• Frequency (f): Number of cycles per second (in Hz).
• Time period (T): Time for one complete cycle, T = 1/f.

5. AC Circuit Elements

• Resistor (R): Current and voltage are in phase.
• Inductor (L): Current lags voltage by 90°.
• Capacitor (C): Current leads voltage by 90°.

6. Impedance (Z)

Effective opposition offered by an AC circuit is called impedance.

In an RLC series circuit:

Z = √(R² + (XL - XC)²)

• Inductive reactance: XL = ωL = 2πfL
• Capacitive reactance: XC = 1 / (ωC) = 1 / (2πfC)

7. Power in AC Circuit

• Instantaneous power: p = vi = Vm Im sin²(ωt)
• Average power: P = Vrms Irms cos φ, where φ is the phase difference between voltage and current.

8. Power Factor

The ratio of actual power consumed to apparent power is called power factor:

Power Factor = cos φ = P / (Vrms Irms)

Power factor lies between 0 and 1.

9. Applications of AC

• Power transmission over long distances
• Domestic and industrial electricity supply
• Operation of transformers and electric motors

10. Important Formulas Summary

Electromagnetic Waves
Class 12 Physics (ISC)

1. Introduction

Electromagnetic waves are waves consisting of oscillating electric and magnetic fields that propagate through space carrying energy.

2. Origin of Electromagnetic Waves

They are produced by accelerating electric charges. Changing electric fields produce magnetic fields and changing magnetic fields produce electric fields, sustaining each other and traveling through space.

3. Nature of Electromagnetic Waves

• Transverse waves — electric and magnetic fields are perpendicular to each other and to the direction of wave propagation.
• Do not require a medium — can travel through vacuum.
• Travel at the speed of light, c = 3 × 10⁸ m/s.

4. Speed of Electromagnetic Waves

The speed is given by:

c = 1 / √(μ₀ ε₀)

where μ₀ is permeability and ε₀ is permittivity of free space.

5. Electromagnetic Spectrum

The entire range of electromagnetic waves arranged according to wavelength or frequency is called the electromagnetic spectrum.

6. Applications of Electromagnetic Waves

• Radio waves: communication, broadcasting
• Microwaves: radar, satellite communication, cooking
• Infrared: thermal imaging, remote controls
• Visible light: sight, photography
• Ultraviolet: sterilization, fluorescence
• X-rays: medical imaging
• Gamma rays: cancer treatment, nuclear physics

7. Key Points

• Electromagnetic waves carry energy and momentum.
• Speed in vacuum is constant: c = 3 × 10⁸ m/s.
• They are transverse waves.
• Electric and magnetic fields oscillate perpendicular to each other and direction of wave travel.

Optics
Class 12 Physics (ISC)

1. Introduction

Optics is the branch of physics that deals with the study of light, its properties, and its interactions with matter.

2. Nature of Light

• Light behaves both as a wave and as a particle (wave-particle duality).
• Speed of light in vacuum, c = 3 × 10⁸ m/s.

3. Reflection of Light

• The angle of incidence equals the angle of reflection.
• Reflection follows the law: Incident ray, reflected ray, and normal lie in the same plane.

4. Refraction of Light

• When light passes from one medium to another, it bends due to change in speed.
• Snell’s Law: n₁ sin θ₁ = n₂ sin θ₂
• Refractive index n = c / v, where v is speed of light in medium.

5. Lenses and Mirrors

• Concave and Convex mirrors: Reflect and form images; mirror formula: 1/f = 1/v + 1/u
• Convex and Concave lenses: Refract and form images; lens formula same as mirror formula.

6. Lens Maker’s Formula

1/f = (n - 1) (1/R₁ - 1/R₂)

Where f = focal length, n = refractive index of lens material, R₁ and R₂ = radii of curvature of lens surfaces.

7. Dispersion of Light

Splitting of white light into its constituent colors due to different refraction angles is called dispersion.

8. Interference of Light

When two or more coherent light waves overlap, they produce a pattern of bright and dark fringes due to constructive and destructive interference.

9. Diffraction of Light

Bending of light waves around edges of obstacles and spreading of waves through narrow openings is diffraction.

10. Polarization

Light waves can oscillate in many planes; polarization restricts oscillation to a single plane.

11. Important Formulas

Dual Nature of Radiation and Matter
Class 12 Physics (ISC)

1. Introduction

The dual nature of radiation and matter refers to the concept that particles such as light and electrons exhibit both wave-like and particle-like properties.

2. Wave Nature of Light

• Light exhibits phenomena such as interference and diffraction, which are characteristics of waves.

3. Particle Nature of Light (Photon Model)

• Light can behave as particles called photons.
• Each photon carries energy E = hf, where h is Planck’s constant and f is frequency.

4. Photoelectric Effect

• When light strikes a metal surface, electrons are emitted if the photon energy exceeds the metal’s work function.
• Explained by Einstein using the particle nature of light.

5. Matter Waves (De Broglie Hypothesis)

Louis de Broglie proposed that matter also exhibits wave properties.

Wavelength associated with a particle of momentum p is given by:

λ = h / p = h / mv

6. Experimental Verification

• Electron diffraction experiments show that electrons create interference patterns confirming their wave nature.

7. Significance

• Wave-particle duality is a fundamental concept in quantum mechanics.
• It explains many phenomena at atomic and subatomic scales.

8. Important Constants

Atoms and Nuclei
Class 12 Physics (ISC)

1. Structure of Atom

Atoms consist of a nucleus containing protons and neutrons, surrounded by electrons in orbitals.

2. Constituents of Atom

• Proton: Positively charged particle, mass ≈ 1.67 × 10^-27 kg.
• Neutron: Neutral particle, mass ≈ 1.67 × 10^-27 kg.
• Electron: Negatively charged particle, mass ≈ 9.11 × 10^-31 kg.

3. Atomic Number (Z)

Number of protons in the nucleus; defines the element.

4. Mass Number (A)

Total number of protons and neutrons in the nucleus.

5. Isotopes

Atoms of the same element with same atomic number but different mass numbers (different number of neutrons).

6. Isobars

Atoms with the same mass number but different atomic numbers.

7. Nuclear Forces

Strong nuclear forces hold the nucleus together, overcoming the electrostatic repulsion between protons.

8. Radioactivity

Spontaneous emission of particles or radiation from unstable nuclei. Types include alpha, beta, and gamma decay.

9. Nuclear Binding Energy

Energy required to break a nucleus into its constituent protons and neutrons.

10. Mass-Energy Equivalence

Given by Einstein’s relation:

E = mc²

Where m is the mass defect and c is the speed of light.

11. Important Constants

Electronic Devices
Class 12 Physics (ISC)

1. Introduction

Electronic devices are components that control the flow of electrons to perform functions like amplification, switching, or rectification.

2. Semiconductor Materials

• Materials with conductivity between conductors and insulators.
• Common semiconductors: Silicon (Si) and Germanium (Ge).

3. Diode

• A PN junction device allowing current to flow in one direction only.
• Used for rectification (conversion of AC to DC).

4. Transistor

• Three-layer semiconductor device: either NPN or PNP type.
• Functions as an amplifier or a switch.

5. Logic Gates

Basic building blocks of digital circuits performing logical operations on inputs.

6. Applications

• Diodes: Rectifiers, signal demodulators.
• Transistors: Amplifiers, switches in digital circuits.
• Logic gates: Computers, calculators, digital electronics.

Communication Systems
Class 12 Physics (ISC)

1. Introduction

Communication systems involve the transmission of information from one place to another using electromagnetic waves.

2. Basic Elements of Communication System

• Transmitter: Converts information into a suitable signal for transmission.
• Channel: Medium through which the signal travels (air, cable, etc.).
• Receiver: Receives and converts the transmitted signal back into useful information.
• Information Source: Originates the message or data to be communicated.

3. Types of Communication

• Analog Communication: Information is transmitted in continuous signals.
• Digital Communication: Information is transmitted in discrete binary signals (0s and 1s).

4. Modulation

Process of varying a carrier wave to encode the information signal for transmission.

5. Importance of Communication Systems

• Enables long-distance transmission of data and information.
• Forms the basis of radio, TV, telephone, and internet communication.

Communication Systems
Basic Concepts, Definitions & Numericals

1. Basic Concepts

• Communication: Process of transmitting information from sender to receiver through a medium.
• Signal: Electrical representation of information.
• Transmitter: Device that encodes and sends information.
• Receiver: Device that receives and decodes information.
• Channel: Medium for signal transmission (air, cable, fiber optics).
• Noise: Unwanted disturbances that distort the signal.
• Modulation: Varying a carrier wave to encode the signal.

2. Important Definitions

3. Example Numericals

Electrostatics Symbols Guide

Magnetic Flux Equation

How to Read the Symbols: